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LT
Syntax
LT(E):same type as E
where E has type IDEAL, MODULE, POLY, or VECTOR.
Summary
the leading term of an object
Description
If E is a polynomial this function returns the leading term of the
polynomial E with respect to the term-ordering of the current ring.
For the leading monomial, which includes the coefficient, use LM
.
example
Use R ::= Q[x,y,z]; -- the default term-ordering is DegRevLex
LT(y^2-xz);
y^2
-------------------------------
Use R ::= Q[x,y,z], Lex;
LT(y^2-xz);
xz
-------------------------------
If E is a vector, LT(E) gives the leading term of E with respect to
the module term-ordering of the current ring. For the leading
monomial, which includes the coefficient, use LM
.
example
Use R ::= Q[x,y];
V := Vector(0,x,y^2);
LT(V); -- the leading term of V w.r.t. the default term-ordering, ToPos
Vector(0, 0, y^2)
-------------------------------
Use R ::= Q[x,y], PosTo;
V := Vector(0,x,y^2);
LT(V); -- the leading term of V w.r.t. PosTo
Vector(0, x, 0)
-------------------------------
If E is an ideal or module, LT(E) returns the ideal or module
generated by the leading terms of all elements of E, sometimes called
the initial ideal or module.
example
Use R ::= Q[x,y,z];
I := Ideal(x-y,x-z^2);
LT(I);
Ideal(x, z^2)
-------------------------------
See Also